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ISSN: 2277-3754 ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
373
Embedded Real-Time Control for DC Multi-Converter
Systems
M. M. Abdel Aziz, A. A. Mahfouz, D. M. Khorshied
Abstract—Tightly regulated closed-loop converters are
problematic when used as a load since they tend to draw constant
power and exhibit negative incremental resistance. This negative
resistance causes stability problems for the feeder system,
whether it is an input filter or another converter. In multi-
converter systems, there are many converters loaded by others.
Therefore, the destabilizing effect of the load converters, which
are considered constant-power loads (CPLs), is a major issue. In
this paper, a novel nonlinear feedback control algorithm
“Enhanced Modified Pulse Adjustment” is introduced. This
technique is used to compensate the destabilizing effect of CPLs.
xPC Target Turnkey is used for real-time testing and validation
of the proposed controller design. Analytical, as well as real-time
power hardware-in-the-loop (PHIL) simulation results of the
controller rapid prototyping achieved constant output voltage
regulation, while maintaining the system stability under different
operating conditions sudden changes.
Index Terms — CPLs, Multi-converter systems, Negative
impedance instability, PHIL.
I. INTRODUCTION
Feeding CPLs may impact the stability and dynamics of
the power electronic converters/systems in automotive and
electrical distribution systems. Because of the nonlinearity
and time dependency of converters and motor drivers, and
because of the negative impedance destabilizing
characteristics of CPLs, classical linear control methods
have stability limitations around the operating points and
are not applicable to these systems. Therefore, digital and
nonlinear stabilizing control methods must be applied to
ensure large-signal stability [1] - [18]. In this paper, a novel
digital control ―Enhanced Modified Pulse Adjustment‖
control technique is introduced and applied to the feeder
converter, which operates in discontinuous conduction
mode (DCM) and drives either CPLs or constant voltage
loads (CVLs) [19].
This control approach treats the converter as a digital
system and achieves output-voltage regulation based on
applying high power pulses (DH) of duty cycle ranges
within DH_L to DH_U, and low power pulses (DL) of duty
cycle ranges within DL_L to DL_U. These upper and lower
limits of DH and DL; DH_U, DH_L, DL_U, and DL_L are
calculated each sampling cycle. The feeder converter is
designed to deliver an output power ranges between Pmin
and Pmax, when its input supply voltage varies between
Vin_min to Vin_max.
Also, this control algorithm evaluates the required duty
cycle (dcal) to achieve the desired output voltage regulation.
The controller chooses to apply this dcal between the limits
of either DH or DL according to the difference between Vo
and Vref. Henceforth, if the measured output voltage (Vo) is
less than the desired value (Vref), the controller chooses to
apply this dcal between DH limits, to increase the amount of
energy delivered to the load. Such that; if DH_L ≤ dcal ≤
DH_U , then the controller will generate dcal, else generates
DH_U. These power pulses are generated sequentially until
reaching the desired output voltage level.
Similarly, when Vo is greater than Vref, the controller
applies dcal between DL limits, to decrease the transferred
energy to the load. Such that; if DL_L ≤ dcal ≤ DL_U then
the controller will generate dcal, else generates DL_U.
The main objective of combining between conventional
PWM techniques in calculating (dcal) and applying it within
limits of either high or low power pulses is to reduce the
output voltage ripples by smoothly reach the desired voltage
level. For large differences between Vo and Vref, the
controller will apply the high or low pulses limits to rapidly
reach Vref value. Then for small differences between Vo and
Vref, the controller generates dcal. Hence, dcal value is used
for fine tuning of the output voltage around Vref, to reach
and keep the desired output voltage value with minimum
ripples.
Therefore, the digital control task is to deliver right
amount of energy to the load by right numbers of state
operations, so the average power delivered matches the
required load power [20]. It relies on simple concepts of the
waveform shaping of the inductor current of the power
converters.
Stability analyses, controller design procedures and
design constraints, as well as real-time power-hardware-in-
the-loop (PHIL) simulation results are depicted for the
feeder buck converter using xPC Target Turnkey. The
system dynamic response under various step changes in the
reference voltage, the input supply voltage, and loading
conditions are studied. Moreover, a comparison between
the proposed controller and previous designs is introduced
to depict the contribution of the proposed control algorithm.
II. MERITS OF THE NOVEL PROPOSED DIGITAL
CONTROL TECHNIQUE
The novel proposed digital control technique features the
following merits:
1- Line and load regulations are simply achievable for
CPLs & CVLs.
2- Fast and smooth dynamic response for a wide
range of operating conditions changes
3- Applicable to all power-electronic converters;
either conventional or integrated topologies loaded by
different load types [5], [7], [13], [14].
ISSN: 2277-3754 ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
374
4- Simple, low cost and ease to develop, using DSPs
or ASIC, as it needs few logic gates and comparators to be
implemented.
5- Robust against variations of the power converter
parameters. Thus handles the actual DC/DC converters
nonlinearities.
6- It is efficient to be used in the advanced
applications which include large number of multi-
converter power systems.
III. STABILITY ANALYSIS OF BUCK
CONVERTER IN DCM
The multi-converter power system is simply
represented by two cascaded levels of DC-DC buck
converters as shown in Fig. 1.
The average inductor current
(1)
Fig. 1 Switching Period of a Dc-Dc Converter in DCM
When the inductor at the charging mode, during ton = d TS:
∵ (2)
& When the inductor at the discharging mode, during tD:
∵ (3)
At steady state conditions, of which our always
consideration, and interest of study not in transients, the
inductor discharging current equals to the inductor charging
current.
(4)
Subst. in
(5)
So,
(6)
(7)
Since the input current increases linearly with the on-time
of the switch, the energy, which is drawn from the input-
power source is equal to
(8)
Duty cycle calculations ( :
In the buck dc/dc converters during the time intervals tonH
= dHT, diode is off; therefore, the output capacitor
discharges through the load, and the magnitude of the
output voltage decreases. During ton = d TS, using the
Kirchoff’s laws, one can write
Solving the differential equation earlier, output-voltage
variations of a buck–boost converter during tonH and tNH in a
high power cycle can
(9)
So, the calculated duty cycle is evaluated as;
(10)
This relationship ensures that any changes in Vo & P
(loading conditions) reflect its direct effect on the duty
cycle. Also the supply input voltage changes indirectly
affect the duty cycle through P & Vo. So, the controller
decides the appropriate switching pattern to regulate the
output voltage.
IV. ENHANCED MODIFIED PULSE
ADJUSTMENT CONTROL ALGORITHM
Ref. [19] proposes the design, verification, and validation
processes of this control algorithm. Nevertheless, the flow
chart of the Enhanced Modified pulse adjustment control
method can be described as follows:
1- Enter the input parameters, such as; Vref, Vin_min,
Vin_max, Pmin, Pmax, fS, Ts and L, C, of the feeder converter.
Fig. 2 Multi-Converter System Prototype Block
diagram
ISSN: 2277-3754 ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
375
2- For each sampling cycle:
1. Measure Vo, io, iL, Vin of the feeder converter.
2. Calculate the operating converter duty cycle, such
that; .
3. Calculate the feeder converter input power using
eq. (8).
4. Output power is equal to the input power,
neglecting the losses, hence assuming 100% power
converter efficiency. Evaluate the required duty cycle "dcal"
is calculated using eq. (10).
5. Using eq. (8), each of DH & DL upper and lower
limits (DH_U , DH_L , DL_U , and DL_L) are calculated each
sampling cycle according to Pmin, Pmax, Vin_min, and Vin_max
such that:
&
(11)
&
(12)
6. According to the error voltage sign; Ve = Vref - Vo ,
the controller chooses to apply " " within the limits of
high power pulses ( ) or Low power pulses
( ).
7. If Ve is positive, so the delivered energy to the
load must be increased. Hence, the controller decides to
apply DH limits. Hence ― ‖ will be limited within DH_U &
DH_L values. Else, the controller decides to apply DL limits,
so " ‖ will be limited within DL_U & DL_L values.
8. These pulses are sequentially applied until the
desired reference voltage is obtained at the output voltage.
V. DCM OPERATION CONSTRAINT
To ensure DCM, the inductor discharge current should be
less than or equal the inductor charging current.
Hence, in order to ensure in the DCM operating
condition, DH_U should not exceed , which is
evaluated as described below:
(13)
For the high power pulses, considering the DCM
constraint limits their values between VCH_L & VCH_max.
Hence in this case the controller may skip evaluating VCH_U
value so save its speed.
VI. EXPERIMENTAL SETUP
The enhanced modified pulse-adjustment control
algorithm was employed to the feeder buck converter. This
converter is loaded with a CPL, represented as tightly
regulated buck converter feeding a resistive load. The
controller of the buck load converter is a conventional PI
controller, implemented using TL494 PWM [21]. The
proposed control algorithm is implemented and tested in
real-time using the xPC target turnkey, as illustrated in Fig.
5. Experimental work was done in Science & Technology
Center of Excellence (STCE) in Automatic Control
Laboratory.
Using the derived formulation in the previous sections, a
prototype conventional dc-dc feeder converter of a step
down buck converter power supply with Vin_min = 5V to
Vin_max= 20V, Pmin = 0.1W to Pmax= 30W.
MATLAB / Simulink is used to simulate the Enhanced
Modified pulse adjustment control technique. Both feeder
and load buck converters are electrically modeled using
"SimPowerSys" toolbox [19]. Table 1: The Proposed Feeder Buck Converter Parameters
Variable Parameter Value
Vin (V) Input voltage 15
Vref (V) Reference output voltage 8
ISSN: 2277-3754 ISO 9001:2008 Certified
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Volume 2, Issue 1, July 2012
376
fS (kHz) Switching frequency 6.25
L (µH) Magnetizing inductance 428
C (µF) Output filter capacitance 330
The sampling frequency is 30 kHz, as the switching
frequency (fs) of the feeder buck converter is 6.25 kHz and
of the load buck converter is 5 kHz. The output control
voltages of the controller will be limited within 0.15V to
3V, which is the practical VC range of TL494 PWM chip as
shown in Fig.5.
VII. EXPERIMENTAL RESULTS
The following experimental results illustrate the
negative impedance characteristics of the tightly regulated
load converter, the design constraints of the controller
parameters. Also, the system dynamic response under step
changes of the reference voltage, the input voltage and the
loading conditions are depicted.
a) CPL CHARACTERISTICS:
Fig. 7 illustrates the incremental negative impedance
characteristics of this load are obviously clear. It is obvious
that increases as the V increases. This is the indicated
feature of CPLs, that impacts the power quality and stability
of the multi-converter systems.
b) DESIGN CONSTRAINTS
For a load of 5W average power, experimental results are
introduced to indicate the appropriate limits for the
Controller input parameters, such as; Pmax, Pmin and
Vin_min. It is worth to mention that the TL494 PWM closed
loop controller of the load buck converter operates for an
input voltage ranges from 7V – to – 40V. Hence it appears
as a CPL at the feeder converter input terminals; exhibits
negative incremental impedance characteristics ;
Fig. 5 Fully Assembled, Power Hardware-in-The-Loop (PHIL) Real-Time Testing For Rapid
Controller Prototyping Using Xpc Target
Fig. 7 Practical Load Negative Impedance Characteristics
Of CPL at Fs = 5 Khz
ISSN: 2277-3754 ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
377
only within this voltage range. Else, the load converter will
be considered as a conventional CVL not a CPL. This is
represented by the case of Vo = 6V, to validate the proposed
controller operation in achieving output voltage regulation
for both loading cases; CVLs and CPLs.
1- Pmax Limitations
Set Pmin = 0.1W, Vin_min = 5V, Vin_max = 20V.
For Pload = 5W; it is observable from Fig. 8 that when Vo
= 8V,
Fig. 8 Effect of Pmax Limits on the Feeder Output Voltage
So Pmax should be at least 15W to deliver the right amount
of energy to the load. I.e., Pmax ≥ 3PLoad , as the load
requires to sink 0.584A from the feeder converter. So the
controller increases the DH limits to increase the energy
delivered to the load. DH limits mainly is a function of Pmax
according to eq. (11). Also, For Vo = 10V, Pmax ≥ 10W and
Vo = 12V, Pmax = 5W. For Vo = 6V, Pmax should be at least
30W to enable proper load supplying. Generally, its
recommended that Pmax ≥ 6 PLoad to satisfy all operating
conditions for either CVLs or CPLs.
2- Pmin limitations
Set Pmax = 30W, Vin_min = 5V, Vin_max = 20V.
Fig. 9 illustrates that, when Vo = 8V, so Pmin should not
exceeds 1W. I.e., Pmin ≤ 0.2PLoad . Otherwise, the output
voltage is dropped to ≈ 6V, so can’t maintain the required
operating voltage. According to eq. (12), DL limits mainly
depends on Pmin value. So when Pmin increases, DL increases
causing the output voltage level to decrease. Also for Vo =
10V, Pmin ≤ 0.4PLoad and Vo = 12V, Pmin ≤ 0.5PLoad For Vo =
6V, there is no significant constraint on Pmin.
Generally, its recommended that Pmin ≤ 0.2PLoad to
satisfy all operating conditions for either CVLs or CPLs.
3- Vin_min limitation
Set Pmax = 30W, Pmin = 0.1V, Vin_max = 20V. According to
(11), (12), DH_U and DL_U are functions of the difference
between the Vin_max and Vref.
Fig. 10 Effect of Vin_Min Limits on the Feeder Output Voltage
Fig. 10 illustrates that for Vo = Vref = 8V, there is no
effect of the Vin_min limits on the output voltage limit. But
for 10V and 12V reference voltages, as the difference
between Vin_max and Vref decreases, the energy transferred to
the load is not sufficient to maintain the required operating
voltage, hence the output voltage drops.
Hence, as the difference between Vin_min and Vref
increases, the feeder converter can deliver the right amount
of energy to the load, thus can keep constant output voltage
at its desired level. Generally, Vin_min limits could be
assumed to be; Vin_min ≤ 0.3 Vin.
c) Effect of Vref step changes on Vo
The following results are recorded relying on adjusting
the controller parameters such that; Vin_min = 5V, Vin_max =
20V, Pmax = 30W, Pmin = 0.1W. It is depicted that when the
output voltage increased from 8V to 10V, the average load
current decreased from 0.556A to 0.472A, and when the
output voltage increased from 10V to 12V, the average load
current decreased from 0.472A to 0.405. So is negative
and increases as Vo increases, which is the incremental
negative impedance characteristics; the worst destabilizing
effect of CPLs.
Fig.11 proved that the proposed controller algorithm
achieves good dynamic response to rapidly track the
variations of the reference voltage, and precisely achieve
the output voltage regulation with minimum voltage ripples,
while maintaining the system stability.
Fig. 9 Effect of Pmin limits on the feeder output voltage
ISSN: 2277-3754 ISO 9001:2008 Certified
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This is achievable by controlling the inductor current
waveform such that; the controller generates the right
number of power pulses of specified duty ratios that
control the transferred energy to the load as depicted in
Fig.12.
d)
d) Effect of Vin step changes on Vo
(a)
(b)
Fig. 11 Dynamic Response of the Proposed Controller for The
Buck Feeder Converter To Reference Voltage Step Changes,
When Vin = 15V; (A) Output Voltage, (B) Inductor Current
(C) Load Current (D) Load Power
(c)
(d)
(e)
Contd’ Fig. 11 (e) Duty ratio and (f) Input voltage
(f)
(e)
(f)
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International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
379
The system dynamic response for Vin step change from
15V to 19V at 3.9S is discussed in this section. The
following results are recorded for the following controller
parameters Vin_min = 5V, Vin_max = 20V, Pmax = 30W, Pmin =
0.1W.
It is noticed that when Vin increased from 15V to 19V,
the converter duty cycle decreased from 0.541 to 0.431 to
maintain constant output voltage; Vo = 8V
Moreover, Fig. 13 shows that the inductor is reshaped to
actuate this control action; to maintain output voltage
regulation while transferring the right amount of energy to
the CPL.
e) Effect of PLoad sudden changes on Vo
The system dynamic response for the loading step
change from 7.2W to 4.46W at 4.2S is below. The
controller parameters are set to Vin_min = 5V, Vin_max = 20V,
Pmax = 30W, Pmin = 0.1W.
(b)
(d)
(c)
(a)
Fig. 13 Dynamic Response of the Proposed Controller for
the Buck Feeder Converter to Input Voltage Step Change
from 15V to 19V, When Vref=8V; (A) Input Voltage B)
Output Voltage, (C) Inductor Current, (D) Load Current.
(a)
Fig. 14 Dynamic response of the proposed controller for
the buck feeder converter to load converter step load
change from 7.2W to 4.46W at 4.2S, when Vref = 8V; (a)
Load power.
Contd' Fig. 13 (e) Load power, and (f) Duty ratio
(f)
Contd' Fig. 14 , (f) Duty cycle
ISSN: 2277-3754 ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
380
Fig. 14 illustrates the system dynamic response in case
of sudden load switching off; the controller then generates
more low power pulses to decrease the transferred energy
to the CPL that maintains regulated output voltage of 8V
with the same duty cycle of 0.54. Agreed with [5], it is
observed that increasing the CPL (decreasing RLoad)
decreases the damping of the LC tank, hence decrease the
output voltage ripples.
f) Stabilizing control of DC/DC converters with
CPLs using Digital Power Alignment technique
A comparative study between the proposed control
algorithm and power alignment controller [7] is
introduced. Experimental results when applying constant
power cycles of VC_H = 2.3 & VC_L = 0.15are shown
below;
The Power Alignment Control algorithm is applied in
this section assuming that the sampling frequency is 30
kHz and the switching frequency of the feeder is 6.25 kHz.
So, they are not synchronized as mentioned in the previous
work. Comparing Fig. 15 to Fig. 12, it is obvious that the
output voltage ripples is decreased when using the
proposed control algorithm, also the settling time here is
0.04S while in Fig. 12 it was 0.018S. So it achieves faster
system response to track Vref step changes smoothly with
less overshoot.
VIII. CONCLUSION
In this paper, a novel digital control technique
―Enhanced Modified Pulse Adjustment‖ is introduced. It is
(d)
(e)
Contd' Fig. 14 , (b) the output voltage; (c) the inductor
current (d) Load current, (e) Input voltage and
(f) Duty cycle
(b)
(c)
Fig. 15 Inductor current waveform when
Vo changes from 12V to 10V using power
alignment control algorithm
ISSN: 2277-3754 ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
381
used to achieve the required output voltage regulation of a
dc/dc buck converter driving a CPL. It is applied to
compensate the destabilizing impact of the CPL negative
incremental resistance on its feeder convert. This proposed
fixed frequency control algorithm was implemented in real-
time using the xPC target turnkey. This method is
applicable to all power-electronic converters topologies,
driving different load types. In spite of its simplicity, it has
robust, fast and smooth dynamic response to maintain
constant output voltage in spite of any sudden changes of
the operating conditions.
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[5] A. M. Rahimi, " Addressing negative impedance instability problem of constant power loads: comprehensive view
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[6] A. Khaligh, and A. Emadi, ―Mixed DCM/CCM Pulse Adjustment with Constant Power Loads,‖ IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 766-782, April 2008.
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BIBLIOGRAPHY
Mohamed Mamdouh Abdel Aziz is
professor of electrical power and machines.
He has a B.Sc. in electrical power and
machines, distinction and first class honors,
Cairo University, Giza, Egypt, 1970.
Following graduation he was an instructor in
the Department of Electrical Power and
Machines, at Cairo University from 1970 to
1972. He has a M.Sc. in electrical power and
machines, Cairo University, Giza, Egypt,
1972. Following graduation he was a teaching
assistant in the Department of Electrical
Power and Machines, at Cairo University from 1972 to 1975. He has a
Ph.D. in electrical power and machines, Cairo University, Giza, Egypt,
ISSN: 2277-3754 ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
382
1975. He is currently a professor in the Department of Electrical Power
and Machines, at Cairo University. Dr. Abdel Aziz has been member of the
Institute of Electrical and Electronics Engineers. On the technical side Dr.
Abdel Aziz is author or co-author of many refereed journal and conference
papers. Areas of research include cables, contact resistance, harmonics,
power quality, photovoltaic systems, and wind energy systems.
Ahmed A. Mahfouz received the B.Sc.
degree in electrical engineering with the
emphasis on power electronics in 1981, the
M.S. degree in power electronics in 1987 both
from Cairo University, Egypt, and the Ph.D.
in power electronics in 1991, through a
channel program funded by DAAD between
Cairo University (Egypt) and Wuppertal
University (Germany) in 1991. Since 1991,
he has been on the faculty of Engineering,
Cairo University, where he served as
Lecturer. 1992 to 1993 he was on scientific
leave from Cairo University to Calgary University (Canada).
From 1998 to 2005 he served as an Associate Professor at Cairo
University. From 2005 till now he is a full Professor at Cairo University.
He served as Technical Director of Siemens Automation Lab at Faculty of
engineering, Cairo University. He is currently involved in landmine
detection project. His research interests include power electronics,
microcontrollers and DSP programming, measurements, industrial
automation, renewable energy, and power quality. He has authored over 60
technical publications..
Dina Mamdooh Khorshied received the B.Sc. degree in electrical power
and machines, Cairo University, Giza, Egypt, 1999. She had the M.Sc.
degree in electrical power and machines, Cairo University, Giza, Egypt,
2006. Practically, she worked in the field of AC-to-DC electric traction
substations. Currently, she is working in the automatic control research
laboratory at Science and Technology Center of Excellence (STCE) ,
Egypt. Areas of research include harmonic filters design for power
systems, analog & digital controllers design, verification and validation;
including system analysis, modeling, simulation and real time
implementation.